Properties

 Label 19600.o Number of curves 2 Conductor 19600 CM no Rank 2 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19600.o1")

sage: E.isogeny_class()

Elliptic curves in class 19600.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.o1 19600bx2 [0, 1, 0, -196408, 33439188] [] 103680
19600.o2 19600bx1 [0, 1, 0, -408, 119188] [] 34560 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 19600.o have rank $$2$$.

Modular form 19600.2.a.o

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{9} - 3q^{11} - 5q^{13} - 6q^{17} + q^{19} + O(q^{20})$$

Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.